Elliptic Boundary Value Problems on Corner Domains

Smoothness and Asymptotics of Solutions

  • Authors
  • Monique Dauge

Part of the Lecture Notes in Mathematics book series (LNM, volume 1341)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Monique Dauge
    Pages 2-7
  3. Monique Dauge
    Pages 8-24
  4. Monique Dauge
    Pages 26-57
  5. Monique Dauge
    Pages 58-103
  6. Monique Dauge
    Pages 104-127
  7. Monique Dauge
    Pages 128-152
  8. Monique Dauge
    Pages 153-170
  9. Back Matter
    Pages 214-261

About this book

Introduction

This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and semi-Fredholm properties of induced operators are completely characterized. By specially choosing the classes of operators and domains and the functional spaces used, precise and general results may be obtained on the smoothness and asymptotics of solutions. A new type of characteristic condition is introduced which involves the spectrum of associated operator pencils and some ideals of polynomials satisfying some boundary conditions on cones. The methods involve many perturbation arguments and a new use of Mellin transform. Basic knowledge about BVP on smooth domains in Sobolev spaces is the main prerequisite to the understanding of this book. Readers interested in the general theory of corner domains will find here a new basic theory (new approaches and results) as well as a synthesis of many already known results; those who need regularity conditions and descriptions of singularities for numerical analysis will find precise statements and also a means to obtain further one in many explicit situtations.

Keywords

BVP Boundary value problem Laplace operator Smooth function Sobolev space operator

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0086682
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50169-5
  • Online ISBN 978-3-540-45942-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book